{
 "metadata": {
  "name": "",
  "signature": "sha256:a8608c57074e399af9cec1d0b0764b2676c04fd2c3657add02dfb6506bdda601"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function\n",
      "from deltasigma import *\n",
      "from IPython.core.display import Image"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# skip this, this is just to display nice tables.\n",
      "from itertools import izip_longest\n",
      "class Table(list):\n",
      "    def _repr_html_(self):\n",
      "        html = [\"<table>\"]\n",
      "        for row in self:\n",
      "            html.append(\"<tr>\")\n",
      "            for col in row:\n",
      "                try:\n",
      "                    float(col)\n",
      "                    html.append(\"<td>%.6f</td>\" % col)\n",
      "                except(ValueError):\n",
      "                    html.append(\"<td><b>%s</b></td>\" % col)\n",
      "            html.append(\"</tr>\")\n",
      "        html.append(\"</table>\")\n",
      "        return ''.join(html)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Modulator realization and dynamic range scaling - # demo3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this ipython notebook, the following is demonstrated:\n",
      "\n",
      " * A 5th order delta sigma modulator is synthesized, with optimized zeros and an OSR equal to 42.\n",
      "\n",
      " * We then convert the synthesized NTF into `a`, `g`, `b`, `c` coefficients for the `CRFB` modulator structure.\n",
      " \n",
      " * The maxima for each state are evaluated.\n",
      " \n",
      " * The `ABCD` matrix is scaled so that the state maxima are less than the specified limit.\n",
      "\n",
      " * The state maxima are re-evaluated and limit compliance is checked.\n",
      "\n",
      "**NOTE:** This is an ipython port of `dsdemo3.m`, from the **[MATLAB Delta Sigma Toolbox](http://www.mathworks.com/matlabcentral/fileexchange/19-delta-sigma-toolbox)**, written by Richard Schreier."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Delta sigma modulator synthesis"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "order = 5\n",
      "R = 42\n",
      "opt = 1\n",
      "H = synthesizeNTF(order, R, opt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's inspect the NTF, printing out the transfer function and plotting poles and zeros with respect to the unit circle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(pretty_lti(H))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "        (z^2 - 1.995z + 1) (z^2 - 1.998z + 1) (z - 1)         \n",
        "--------------------------------------------------------------\n",
        " (z^2 - 1.614z + 0.6657) (z^2 - 1.797z + 0.8552) (z - 0.7783) \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(10, 5))\n",
      "plotPZ(H, showlist=True)\n",
      "title('NTF');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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e0K+frg4jhHCcYsV071KrVhAUpNedFsKK3LCjx1C+dkcrpavBXLyoawLLpUhC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\nu/oayNWrwcfH7GiEyD9KwQsv6GGZNWv0AjdCWIm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       "text": [
        "<matplotlib.figure.Figure at 0xb022496c>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Evaluation of the coefficients for a CRFB topology\n",
      "The CRFB topology is depicted in the following diagram."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(url='http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png', retina=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png\"/>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<IPython.core.display.Image at 0xb01c3fec>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since the modulator order is 5, we're interested in the topology for odd order modulators."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Unscaled modulator"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the coefficients"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a, g, b, c = realizeNTF(H)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Feed-in selection\n",
      "We'll use a single feed-in for the input, to have a maximally flat STF.\n",
      "\n",
      "This means setting $\\ b_n = 0, \\ \\forall n > 1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.concatenate((b[0].reshape((1, )), np.zeros((b.shape[0] - 1, ))), axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = Table()\n",
      "ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']\n",
      "t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', \n",
      "          'Feed-in', 'Interstage'])\n",
      "t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])\n",
      "[t.append(x) for x in izip_longest(ilabels, a.tolist(), g.tolist(), b.tolist(), c.tolist(), fillvalue=\"\")]\n",
      "t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td><b>Coefficients</b></td><td><b>DAC feedback</b></td><td><b>Resonator feedback</b></td><td><b>Feed-in</b></td><td><b>Interstage</b></td></tr><tr><td><b></b></td><td><b>a(n)</b></td><td><b>g(n)</b></td><td><b> b(n)</b></td><td><b> c(n)</b></td></tr><tr><td><b>#1</b></td><td>0.000667</td><td>0.001622</td><td>0.000667</td><td>1.000000</td></tr><tr><td><b>#2</b></td><td>0.008583</td><td>0.004593</td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#3</b></td><td>0.055201</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#4</b></td><td>0.247607</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#5</b></td><td>0.556935</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#6</b></td><td><b></b></td><td><b></b></td><td>0.000000</td><td><b></b></td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[['Coefficients',\n",
        "  'DAC feedback',\n",
        "  'Resonator feedback',\n",
        "  'Feed-in',\n",
        "  'Interstage'],\n",
        " ['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'],\n",
        " ('#1',\n",
        "  0.0006670795813848524,\n",
        "  0.001622050471799641,\n",
        "  0.0006670795813848524,\n",
        "  1.0),\n",
        " ('#2', 0.008582635287918602, 0.004592653480622877, 0.0, 1.0),\n",
        " ('#3', 0.055201451644908195, '', 0.0, 1.0),\n",
        " ('#4', 0.24760725165068767, '', 0.0, 1.0),\n",
        " ('#5', 0.5569351152496803, '', 0.0, 1.0),\n",
        " ('#6', '', '', 0.0, '')]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ABCD = stuffABCD(a, g, b, c);\n",
      "u = np.linspace(0, 0.6, 30);\n",
      "N = 1e4; \n",
      "T = np.ones((1, N))\n",
      "maxima = np.zeros((order, len(u)))\n",
      "for i in range(len(u)):\n",
      "    ui = u[i]\n",
      "    v, xn, xmax, _ = simulateDSM(ui*T, ABCD);\n",
      "    maxima[:, i] = np.squeeze(xmax)\n",
      "    if any(xmax > 1e2):\n",
      "        umax = ui;\n",
      "        u = u[:i+1];\n",
      "        maxima = maxima[:, :i]\n",
      "        break;\n",
      "# save the maxima\n",
      "prescale_maxima = np.copy(maxima)\n",
      "print('The state maxima have been evaluated through simulation.')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The state maxima have been evaluated through simulation.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot of the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(order):\n",
      "    semilogy(u, maxima[i, :],'o-')\n",
      "    if not i:\n",
      "        hold(True)\n",
      "grid(True)\n",
      "xlabel('DC input')\n",
      "ylabel('Peak value')\n",
      "title('Simulated State Maxima')\n",
      "xlim([0, 0.6]) \n",
      "ylim([1e-4, 10]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pJ277+WeefestPyM9O4CBNBqXCCQfiqz3NXPfeKPSUF9yiRhLQRAalNo+otV0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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb015626c>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Scaled modulator\n",
      "### Calculate the scaled coefficients"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ABCDs, umax, _ = scaleABCD(ABCD, N_sim=1e5)\n",
      "as_, gs, bs, cs = mapABCD(ABCDs)\n",
      "print('\\nScaled modulator, umax = %.2f\\n' % umax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Scaled modulator, umax = 0.58\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = Table()\n",
      "ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']\n",
      "t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', \n",
      "          'Feed-in', 'Interstage'])\n",
      "t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])\n",
      "[t.append(x) for x in izip_longest(ilabels, as_.tolist(), gs.tolist(), bs.tolist(), cs.tolist(), fillvalue=\"\")]\n",
      "t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td><b>Coefficients</b></td><td><b>DAC feedback</b></td><td><b>Resonator feedback</b></td><td><b>Feed-in</b></td><td><b>Interstage</b></td></tr><tr><td><b></b></td><td><b>a(n)</b></td><td><b>g(n)</b></td><td><b> b(n)</b></td><td><b> c(n)</b></td></tr><tr><td><b>#1</b></td><td>0.100298</td><td>0.008508</td><td>0.100298</td><td>0.135347</td></tr><tr><td><b>#2</b></td><td>0.174656</td><td>0.010817</td><td>0.000000</td><td>0.190649</td></tr><tr><td><b>#3</b></td><td>0.214165</td><td><b></b></td><td>0.000000</td><td>0.380271</td></tr><tr><td><b>#4</b></td><td>0.365304</td><td><b></b></td><td>0.000000</td><td>0.424567</td></tr><tr><td><b>#5</b></td><td>0.348852</td><td><b></b></td><td>0.000000</td><td>1.596478</td></tr><tr><td><b>#6</b></td><td><b></b></td><td><b></b></td><td>0.000000</td><td><b></b></td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[['Coefficients',\n",
        "  'DAC feedback',\n",
        "  'Resonator feedback',\n",
        "  'Feed-in',\n",
        "  'Interstage'],\n",
        " ['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'],\n",
        " ('#1',\n",
        "  0.10029776281163674,\n",
        "  0.008508036472572998,\n",
        "  0.10029776281163674,\n",
        "  0.13534708993976094),\n",
        " ('#2', 0.17465586699408495, 0.010817262165527199, 0.0, 0.1906492146605832),\n",
        " ('#3', 0.21416477448908453, '', 0.0, 0.3802708889018403),\n",
        " ('#4', 0.3653036244466539, '', 0.0, 0.4245670864166437),\n",
        " ('#5', 0.34885226443464945, '', 0.0, 1.5964784294929264),\n",
        " ('#6', '', '', 0.0, '')]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = np.linspace(0, umax, 30)\n",
      "N = 1e4\n",
      "T = np.ones((N,))\n",
      "maxima = np.zeros((order, len(u)))\n",
      "for i in range(len(u)):\n",
      "    ui = u[i]\n",
      "    v, xn, xmax, _ = simulateDSM(ui*T, ABCDs)\n",
      "    maxima[:, i] = xmax.squeeze()\n",
      "    if any(xmax > 1e2):\n",
      "        umax = ui;\n",
      "        u = u[:i]\n",
      "        maxima = maxima[:, :i]\n",
      "        break\n",
      "print('The state maxima have been re-evaluated through simulation.')\n",
      "print(\"The maximum input was found to be %.6f\" % umax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The state maxima have been re-evaluated through simulation.\n",
        "The maximum input was found to be 0.583333\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot of the state maxima after scaling"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(order):\n",
      "    semilogy(u, maxima[i, :], 'o-')\n",
      "    if not i:\n",
      "        hold(True)\n",
      "grid(True)\n",
      "ylabel('Peak value')\n",
      "xlabel('DC input')\n",
      "xlim([0, 0.6])\n",
      "ylim([4e-2, 4]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iDj1zCGuhVR00LbBgLbSysHgBY7C/4OqZkmeYz2z+Mj4Pr7Xfw5yfoWdPWjTL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\n2dx6dN8+JTEtze3NuvUrVyq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       "text": [
        "<matplotlib.figure.Figure at 0xb15a0fac>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### System version information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py\n",
      "%load_ext version_information\n",
      "%reload_ext version_information\n",
      "\n",
      "%version_information numpy, scipy, matplotlib, deltasigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.7 (default, Jun  3 2014, 23:36:29) [GCC 4.8.2]</td></tr><tr><td>IPython</td><td>2.1.0</td></tr><tr><td>OS</td><td>posix [linux2]</td></tr><tr><td>numpy</td><td>1.8.1</td></tr><tr><td>scipy</td><td>0.14.0</td></tr><tr><td>matplotlib</td><td>1.3.1</td></tr><tr><td>deltasigma</td><td>0.1-4</td></tr><tr><td colspan='2'>Tue Jun 24 18:04:28 2014 CEST</td></tr></table>"
       ],
       "json": [
        "{\"Software versions\": [{\"version\": \"2.7.7 (default, Jun  3 2014, 23:36:29) [GCC 4.8.2]\", \"module\": \"Python\"}, {\"version\": \"2.1.0\", \"module\": \"IPython\"}, {\"version\": \"posix [linux2]\", \"module\": \"OS\"}, {\"version\": \"1.8.1\", \"module\": \"numpy\"}, {\"version\": \"0.14.0\", \"module\": \"scipy\"}, {\"version\": \"1.3.1\", \"module\": \"matplotlib\"}, {\"version\": \"0.1-4\", \"module\": \"deltasigma\"}]}"
       ],
       "latex": [
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 2.7.7 (default, Jun  3 2014, 23:36:29) [GCC 4.8.2] \\\\ \\hline\n",
        "IPython & 2.1.0 \\\\ \\hline\n",
        "OS & posix [linux2] \\\\ \\hline\n",
        "numpy & 1.8.1 \\\\ \\hline\n",
        "scipy & 0.14.0 \\\\ \\hline\n",
        "matplotlib & 1.3.1 \\\\ \\hline\n",
        "deltasigma & 0.1-4 \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Tue Jun 24 18:04:28 2014 CEST} \\\\ \\hline\n",
        "\\end{tabular}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "Software versions\n",
        "Python 2.7.7 (default, Jun  3 2014, 23:36:29) [GCC 4.8.2]\n",
        "IPython 2.1.0\n",
        "OS posix [linux2]\n",
        "numpy 1.8.1\n",
        "scipy 0.14.0\n",
        "matplotlib 1.3.1\n",
        "deltasigma 0.1-4\n",
        "<tr><td colspan='2'>Tue Jun 24 18:04:28 2014 CEST</td></tr>"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}